Values of the log-posterior

Modeling
1

Hi all,

I have a general question regarding STAN-Sampling.

When sampling from a univariate normal distribution, I obtain MCMC-samples x_1,...,x_R from which I can obtain the logposterior-value. Plotting the histogram of these leads to the following plot (like the lp__-Histogram in the pairs plot). This makes sense to me: Most of the samples lie where the density is the highest.

grafik

However, when looking at a general example model, the histogram of the log-posterior has a very different form, more like a bell-shape. It seems like a lot less samples lie in regions with a high density value (>-110) and most samples lie in regions with density values around -115. Why is that the case?

grafik
grafik752×622 104 KB

In my specific example, the posterior has two modes and I plot the histograms of the sampled lp-values for both modes separately. Here again, I have bellshaped curves. However, I conclude that the mode corresponding to the grey histogram is the higher and hence desirable mode. Is that correct?

grafik

Thank you for your thoughts,
Ariane

2

because the region of high likelihood is comparably quite small.